%I #37 Sep 08 2022 08:46:13
%S 1,1,4,186624,248907105618907424441185380787996852224
%N Product of the first n ultrafactorials ((n!)^(n!)).
%C a(6) is about 10^2345.
%C This could be called a superultrafactorial by analogy with factorial and superfactorial.
%H Matthew Campbell, <a href="/A260614/b260614.txt">Table of n, a(n) for n = 0..5</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F a(n) = Product_{k=1..n} A046882(k).
%e a(3) = (1!)^(1!) * (2!)^(2!) * (3!)^(3!) = 1^1 * 2^2 * 6^6 = 1 * 4 * 46656 = 186624.
%t Table[Product[(m!)^(m!), {m, 0, n}], {n, 0, 5}]
%o (PARI) a(n)=prod(k=2,n,k!^k!) \\ _Charles R Greathouse IV_, Aug 14 2015
%o (Magma) [Factorial(n)^Factorial(n): n in [0..5]]; // _Vincenzo Librandi_, Aug 29 2015
%Y Cf. A000178, A046882.
%K nonn,easy
%O 0,3
%A _Matthew Campbell_, Aug 13 2015